$\dfrac{ -4g - 4h }{ 2 } = \dfrac{ -g + 10i }{ 4 }$ Solve for $g$.
Multiply both sides by the left denominator. $\dfrac{ -4g - 4h }{ {2} } = \dfrac{ -g + 10i }{ 4 }$ ${2} \cdot \dfrac{ -4g - 4h }{ {2} } = {2} \cdot \dfrac{ -g + 10i }{ 4 }$ $-4g - 4h = {2} \cdot \dfrac { -g + 10i }{ 4 }$ Multiply both sides by the right denominator. $-4g - 4h = 2 \cdot \dfrac{ -g + 10i }{ {4} }$ ${4} \cdot \left( -4g - 4h \right) = {4} \cdot 2 \cdot \dfrac{ -g + 10i }{ {4} }$ ${4} \cdot \left( -4g - 4h \right) = 2 \cdot \left( -g + 10i \right)$ Distribute both sides ${4} \cdot \left( -4g - 4h \right) = {2} \cdot \left( -g + 10i \right)$ $-{16}g - {16}h = -{2}g + {20}i$ Combine $g$ terms on the left. $-{16g} - 16h = -{2g} + 20i$ $-{14g} - 16h = 20i$ Move the $h$ term to the right. $-14g - {16h} = 20i$ $-14g = 20i + {16h}$ Isolate $g$ by dividing both sides by its coefficient. $-{14}g = 20i + 16h$ $g = \dfrac{ 20i + 16h }{ -{14} }$ All of these terms are divisible by $2$ Divide by the common factor and swap signs so the denominator isn't negative. $g = \dfrac{ -{10}i - {8}h }{ {7} }$